A tutorial review of a classic paper by Samuel J. Mason (1954) is described. That paper contained the first definition of a unilateral power gain for a linear two-port and the first proof that this grain is invariant with respect to linear lossless reciprocal four-port embeddings, thereby making it useful as a figure of merit intrinsic to the device. In this work, that original paper is brought up to date, a tutorial exposition of its contents is presented in a modern form, and its significance and applications in microwave engineering are discussed. The subsequent advances in the subject area are summarized, so that the original paper can be placed within a broader context and understood with a more general perspective. >

Power gain in feedback amplifiers, a classic revisited

The purpose of this paper is three-fold. First, the subject of maximum available power gain at high frequencies is discussed briefly. Also, maximum gain for a four-terminal network driven by a generator having a purely resistive internal impedance is calculated in terms of small-signal parameters of the network. Then a theoretical model of a junction transistor comprising the ideal one-dimensional model plus a base impedance, which may be complex and frequency-dependent as in the case of grown-junction transistors, is introduced for the network to obtain an expression for maximum available power gain in terms of fundamental device parameters. Experimental results, which are given for a number of grown-junction transistors, tend to confirm the theoretical expression. Finally, an idealized model of a grown-junction transistor is introduced, and theoretical power gain is calculated in terms of physical parameters. Such calculations show, for example, that 30 db of gain should be available at 5 mc and that such transistors should be capable of oscillating up to several hundred mc.

High-Frequency Power Gain of Junction Transistors

In this survey paper the various methods used to describe the electric-circuit properties of a transistor are reviewed. After a brief introduction and discussion of the low-frequency characterization of transistors and of the representation used for point-contact transistors, the remainder of the paper is devoted to the subject of high-frequency representation for junction transistors. The more popular equivalent circuits are described, and relations between parameters of different equivalent circuits are given. The alternative procedure of characterizing a transistor by its quadripole parameters (or matrix elements) as a function of frequency also is described, and advantages of this procedure are indicated. Throughout the paper a distinction is made between device parameters, or electrical parameters that can be related to the structure of the transistor as a device, independent of its circuit configuration, and circuit, or terminal, parameters, which correspond to relations between terminal voltages and currents. Included are references to approximately 90 papers representing the work of 60 authors.

Electric Network Representation of Transistors-A Survey

We develop an approximate frequency-independent equivalent circuit for integrated inductors on semiconducting substrates All values of LCR in the equivalent circuit can be calculated directly from inductor geometry The equivalent circuit captures: the skin effect, the proximity effect, the substrate capacitive loss, and the distributed capacitance With careful definition of inductor quality factor, we are able to calculate the contribution of substrate capacitive loss and benefits of a substrate shield Our model was put to test by successfully predicting the published quality factors of various inductors and proving that their geometries are close to optimum

Approximate Equivalent Circuits to Understand Tradeoffs in Geometry of On-Chip Inductors

The transient response of the exact current transfer function, \alpha(\omega) , of a grounded-base junction transistor operating in the short-circuited output condition is compared with the transient response derived from the conventional approximate form for \alpha(\omega) . The response to both a unit impulse and a unit step is calculated, and it is shown how the results may be readily adapted to yield a rapid oscilloscope method of determining the \alpha cutoff frequency and several of the transistor material and dimensional constants.

Solution of a Transistor Transient Response Problem

The analytical solution of the diffusion equation has been used to construct an accurate equivalent circuit of the junction transistor. All network components are expressed in terms of the physical parameters of the transistor. This network has been used to calculate Mason's U-function, which in turn gives the highest frequency at which a transistor can give a power gain. From the derived formula, it is possible to see how the physical parameters interact to limit the frequency response. The design requirements for a given maximum frequency can be obtained from the formulas; a few examples are discussed. The accurate equivalent circuit will be helpful in designing transistors for more specialized applications.

R. A. Pucel

Papers

Design Considerations of Junction Transistors at Higher Frequencies: Based upon an Accurate Equivalent Circuit